An order of n = 3,000 transistors is received. The probability that each transistor is defective is p = 0.001. What is the probability that

P(0)=   $${{\mathtt{0.999}}}^{{\mathtt{3\,000}}} = {\mathtt{0.049\: \!712\: \!393\: \!998\: \!036\: \!3}}$$

 

P(1)=   nCr(3000,1)*0.001*0.999^2999

 

P(2)=    nCr(3000,2)*0.001^2*0.999^2998

 

P(3)=    nCr(3000,3)*0.001^3*0.999^2997

 

P(4)=    nCr(3000,4)*0.001^4*0.999^2996

 

P(5)=    nCr(3000,5)*0.001^5*0.999^2995

 

P(6)=    nCr(3000,6)*0.001^6*0.999^2994

 

work those out and add them up.

 

this calc was baulking - might do better in Wolfram|Alpha calcualtor